Is it possible to have separate animations, with independent timelines?
Yeah, open the timeline and the dope sheet:



On the bottom bar of the dope sheet windon change the "mode" from "Dope sheet" to "Action". Select a door, add an action and call it like "Door 1" and animate it from frame 0 the door opening.

Repeat until you have all doors and windows opening at the same time (only the beggining, you can have different ending times).

Then change the Dope Sheet window to the NLA Editor where you can see all actions:



Press the icon of the down arrows and you'll see that it creates a box, repeat for every object and then, choosing a box and pressing "g" you can move the box freely.